A.2B Practice w/ Calc hints

Front

What is the slope-intercept form of a linear equation?

Back

The slope-intercept form is given by the equation y = mx + b, where m is the slope and b is the y-intercept.

Front

How do you find the slope of a line given two points (x1, y1) and (x2, y2)?

Back

The slope (m) is calculated using the formula m = (y2 - y1) / (x2 - x1).

Front

What does the slope of a line represent?

Back

The slope represents the rate of change of y with respect to x; it indicates how steep the line is.

Front

What is the point-slope form of a linear equation?

Back

The point-slope form is given by y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope.

Front

If a line has a slope of 12, what does this indicate about its steepness?

Back

A slope of 12 indicates a very steep line, meaning for every 1 unit increase in x, y increases by 12 units.

Front

How do you write the equation of a line given a slope and a point?

Back

Use the point-slope form: y - y1 = m(x - x1), substituting the slope (m) and the coordinates of the point (x1, y1).

Front

What is the significance of the y-intercept in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis, represented by the value of b in the slope-intercept form y = mx + b.

Front

How can you verify if a point lies on a given line?

Back

Substitute the x-coordinate of the point into the equation of the line. If the resulting y-value matches the y-coordinate of the point, it lies on the line.

Front

What does a negative slope indicate about a line?

Back

A negative slope indicates that as x increases, y decreases, meaning the line descends from left to right.

Front

What is the formula to convert from point-slope form to slope-intercept form?

Back

To convert, solve for y: y - y1 = m(x - x1) becomes y = mx - mx1 + y1.